Emergence of macroscopic directed motion in populations of motile colloids

Abstract

From the formation of animal flocks to the emergence of coordinated motion in bacterial swarms, populations of motile organisms at all scales display coherent collective motion. This consistent behaviour strongly contrasts with the difference in communication abilities between the individuals. On the basis of this universal feature, it has been proposed that alignment rules at the individual level could solely account for the emergence of unidirectional motion at the group level1,2,3,4. This hypothesis has been supported by agent-based simulations1,5,6. However, more complex collective behaviours have been systematically found in experiments, including the formation of vortices7,8,9, fluctuating swarms7,10, clustering11,12 and swirling13,14,15,16. All these (living and man-made) model systems (bacteria9,10,16, biofilaments and molecular motors7,8,13, shaken grains14,15 and reactive colloids11,12) predominantly rely on actual collisions to generate collective motion. As a result, the potential local alignment rules are entangled with more complex, and often unknown, interactions. The large-scale behaviour of the populations therefore strongly depends on these uncontrolled microscopic couplings, which are extremely challenging to measure and describe theoretically. Here we report that dilute populations of millions of colloidal rolling particles self-organize to achieve coherent motion in a unique direction, with very few density and velocity fluctuations. Quantitatively identifying the microscopic interactions between the rollers allows a theoretical description of this polar-liquid state. Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic ‘flock’, at low densities, or in that of a homogenous polar phase, at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations that were hitherto considered the hallmark of populations of self-propelled particles2,3,17. Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion.

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Figure 1: Single-roller dynamics.
Figure 2: Transition to directed collective motion.
Figure 3: Propagating-band state.
Figure 4: Polar-liquid state.

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Acknowledgements

We acknowledge support from the Paris Emergence programme (D.B.), C’Nano IdF (D.B.) and the Institut Universitaire de France (D.B.). We thank L. S. Tuckerman and H. Chaté for their useful comments and suggestions.

Author information

A.B. and N.D. performed the experiments. A.B., N.D., O.D. and D.B. analysed the experimental results. D.B. conceived the project and designed the experiments. J.-B.C. and D.B. worked out the theory and wrote the Supplementary Methods. J.-B.C., O.D. and D.B. wrote the paper.

Correspondence to Denis Bartolo.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Text and Data, Supplementary Figures 1-8 and additional references. Additional information is given about the theoretical results outlined in the main paper and the transition to collective motion, and the properties of the polar phases, are investigated from a microscopic model. (PDF 515 kb)

Isotropic state (close view)

E0/EQ = 1.39, Φ0=6x10-4, L=72.6 mm, W=1.0 mm, acquisition rate 180 fps, video frame rate18 fps. (MOV 7475 kb)

Band propagation in a racetrack-shaped confinement

E0/EQ = 1.39, Φ0~10-2, L=72.6 mm, W=1.0 mm, acquisition rate 50 fps, video frame rate 200 fps. (MOV 7427 kb)

Band propagation in a racetrack-shaped confinement (close view)

E0/EQ = 1.39, Φ0~10-2, L=72.6 mm, W=1.0 mm, acquisition rate 180 fps, video frame rate 18 fps. (MOV 7810 kb)

A polar liquid spontaneously flowing in a racetrack-shaped confinement (close view)

E0/EQ = 1.39, Φ0=1.8x10-1, L=72.6 mm, W=1.0 mm, acquisition rate 180 fps, video frame rate 18 fps. (MOV 7521 kb)

Bouncing band in a rectangular confinement.

E0/EQ = 1.39, Φ0=1.1x10-1, L=20 mm, W=1.0 mm, acquisition rate 50 fps, video frame rate fps. (MOV 2554 kb)

A one-million-roller population in a square confinement. Large field of view and zoom in

E0/EQ = 1.39, Φ0=1.1x10-1, L=10 mm, W=10 mm, acquisition rate 25 fps, video frame rate 25 fps. (MOV 27182 kb)

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Bricard, A., Caussin, J., Desreumaux, N. et al. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98 (2013). https://doi.org/10.1038/nature12673

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